{"ID":23475890,"CreatedAt":"2026-09-18T01:09:05.407443952Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19394","arxiv_id":"2609.19394","title":"Strategyproof Aggregation in Euclidean Spaces: Rigidity and Median Optimality","abstract":"We study deterministic strategyproof aggregation in finite-dimensional Euclidean spaces. For every odd number $n\\ge3$ of agents and every finite dimension, we prove that the coordinate-wise median minimizes the worst-case approximation ratio for total Euclidean distance among all continuous, anonymous, deterministic strategyproof mechanisms. The same optimality result holds for every even $n\\ge4$ when each coordinate uses a fixed choice of the lower or upper middle rank. The proof combines a rigidity theorem with a normalization that does not increase the approximation ratio: any hypothetical mechanism outperforming the median has a normalized representative that is a fixed coordinate-wise order-statistic rule in a single orthonormal frame. A reflection argument then shows that no such rule improves on the median.","short_abstract":"We study deterministic strategyproof aggregation in finite-dimensional Euclidean spaces. For every odd number $n\\ge3$ of agents and every finite dimension, we prove that the coordinate-wise median minimizes the worst-case approximation ratio for total Euclidean distance among all continuous, anonymous, deterministic st...","url_abs":"https://arxiv.org/abs/2609.19394","url_pdf":"https://arxiv.org/pdf/2609.19394v1","authors":"[\"Jianhao Jia\"]","published":"2026-09-16T20:25:08Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}